Bernie Sanders booed by his own supporters for backing Clinton

Bernie Sanders addresses supporters at the 2016 US Democratic National Convention in Philadelphia, Pennsylvania (Reuters)

The US Democratic National Committee has formally apologised to Senator Bernie Sanders after leaked emails suggested the party's leadership had worked to sabotage his presidential campaign.

"On behalf of everyone at the DNC, we want to offer a deep and sincere apology to Senator Sanders, his supporters, and the entire Democratic Party for the inexcusable remarks made over email," the DNC said in a statement on the opening day of the party's convention in Philadelphia.

It said the emails did not reflect the committee's "steadfast commitment to neutrality during the nominating process".

Mr Sanders urged his supporters to vote for Hillary Clinton in her White House bid as the convention kicked off, drawing jeers and shouts of "We want Bernie" in a show of discord.

The boos underscored the deeply felt anger his convention delegates feel at both Ms Clinton's win and embarrassing emails leaked suggesting the party leadership had worked to sabotage Mr Sanders' campaign for the nomination.

Debbie Wasserman Schultz resigned as party chairwoman on Sunday (local time), a day before the start of the Philadelphia convention to formally nominate Clinton for the November 8 election, and on Monday she bowed to pressure and agreed not to open the convention.

Speaking to his supporters, Sanders savaged Republican presidential candidate Donald Trump, calling him a danger to the future of the country who "must be defeated".

But some in the room booed when he said "we have got to elect Hillary Clinton" and her vice presidential running mate, US Senator Tim Kaine of Virginia.

Mr Sanders, a US senator from Vermont, tried to calm them down. "Brothers and sisters, this is the real world that we live in," he said, adding, "Trump is a bully and a demagogue."

Bernie Sanders addresses his supporters (AAP)

Members of the crowd started screaming back: "So is Hillary."

"She stole the election!" someone else shouted.

The leak on Friday of more than 19,000 Democratic National Committee emails by the WikiLeaks website put the spotlight back on Sanders' failed bid to win the Democratic nomination, and in particular on his complaints during the campaign that the party establishment was working to undermine him.

A self-described democratic socialist, Mr Sanders ran an unexpectedly tough race against former Secretary of State Ms Clinton, galvanising young and liberal voters with his calls to rein in Wall Street and eradicate income inequality.

On Monday (local time), Mr Sanders brought the loudest cheers when he noted that Wasserman Schultz, a US senator from Florida, had resigned as the Democratic National Committee chairman over the email controversy.

"Her resignation opens up the possibility of new leadership at the top of the Democratic Party," Mr Sanders said, adding that the leadership should be made up of "people who want real change."

As Ms Schultz herself spoke to the Democratic delegation from her home state, Florida, she struggled to be heard above boos as she.

"I have decided that in the interest of making sure that we can start the Democratic convention on a high note that I am not going to gavel in the convention," she said.

Protesters held up signs that read "Bernie" and "E-MAILS" and shouted "Shame," as she spoke on Monday (local time).

Others at the meeting cheered and clapped for Ms Schultz, who promised to work hard to help Ms Clinton win over Mr Trump in the November 8 election.

"We know that the voices in this room that are standing up and being disruptive, we know that is not the Florida we know. The Florida we know is united," the congresswoman shouted over the noise of the crowd.

It was an embarrassing prelude to the convention in Philadelphia, which Democratic officials had hoped would convey no-drama competence in contrast to the volatile campaign of Mr Trump. The New York businessman was formally nominated for president at a chaotic Republican convention in Cleveland last week.

At least one national opinion poll showed Mr Trump benefiting from a convention "bump" and pulling just ahead of Ms Clinton, having lagged her for months.

The cache of emails leaked by WikiLeaks disclosed that DNC officials explored ways to undercut Mr Sanders' insurgent presidential campaign, including raising questions about whether Mr Sanders, who is Jewish, was an atheist.

While Mr Sanders has endorsed Ms Clinton, she faces the task of winning over his backers as she battles Mr Trump.

His supporters were already dismayed last week when Mr Clinton passed over liberal favourites like US Senator Elizabeth Warren of Massachusetts to select the more moderate US Senator Tim Kaine of Virginia as her vice presidential running mate.

A Bernie Sanders supporter (Getty)

The Clinton camp questioned whether Russians may have had a hand in the hack attack on the party's emails in an effort to help Mr Trump, who has exchanged words of praise with Russian President Vladimir Putin.

The FBI said on Monday (local time) it would investigate the nature and scope of the hack.

"A compromise of this nature is something we take very seriously, and the FBI will continue to investigate and hold accountable those who pose a threat in cyberspace," the FBI said in a statement.

Separately, the US House of Representatives intelligence committee has been briefed on the hack and would seek information on any potential connection to Russia or another state, said Representative Adam Schiff, the senior Democrat on the panel.

Ms Clinton's campaign manager Robby Mook told CNN that the emails were released by suspected Russian hackers in order to sow discord at the convention and help Republican nominee Mr Trump, her rival in the November 8 presidential election.

The Trump campaign dismissed the allegation as absurd.

A CNN/ORC opinion poll on Monday gave Mr Trump a three-point lead over former secretary of state Ms Clinton, 48 percent to her 45 percent in a two-way presidential matchup. The survey was conducted July 22-24 and had a margin of error of 3.5 percentage points.